College Math Placement Practice Test

By how many dollars would the median cost of three poster prints change if a fourth print costing $45 was added?

1. $5

2. $4

3. $2

4. No change

The correct answer is: $5

To understand how the median cost of three poster prints changes with the addition of a fourth print costing $45, it's essential to first define what the median is. The median is the middle value of a data set when it is organized in ascending order. For a set with an odd number of values, it is simply the central number, whereas for an even number of values, it is the average of the two central numbers. Assuming we have three prints with their costs, let's denote them as \( P_1, P_2, \) and \( P_3 \) in ascending order. The median of these three prints would be the middle value, \( P_2 \). When a fourth print that costs $45 is added, we need to determine how this new print impacts the arrangement of costs and therefore the median. There are several scenarios depending on the values of \( P_1, P_2, \) and \( P_3 \): 1. If $45 is less than \( P_1 \): The costs would be arranged as \( 45, P_1, P_2, P_3 \), and the new median would be the average of \( P_1 \) and \( P